I think too many turkey hunters over complicate things. I have killed a ton of turkey with a 20 gauge 870 and factory full choke barrel. Lately, I kill them with a 20 gauge flintlock trade gun with a cylinder bore.
Any shotgun works if you take time to pattern the gun and load and learn to call turkey. If you don't want to call them in close, may as well shoot them with a rifle.
That's how I see it. Your mileage may differ and that's OK too.
